People often lie across a sofa; that is, with their head resting on a standard armrest of the sofa and their bodies stretched lengthwise across the sofa, from armrest to armrest. Lying this way, at times, is for comfort and at other times, is for viewing TV or conversing with someone located generally seated near an opposite armrest of the sofa so that both people are seated likewise on the sofa facing each other.
Generally, when a person is seated in such a manner, he can use the back of the sofa as an armrest for one arm though it is not at a comfortable height for long term seating; and, there is no corresponding armrest for the other arm nor upper back support. The only option is to attempt to provide support for the otherwise unsupported arm using a firm cushion or other object that is unconnected to the couch such as a pillow, table or another article of furniture.